SOLUTION: amount of a radioactive tracer remaining after t days is given by A=A0e^-0.058t, where A0 is the starting amount at the beginning of the time period. how many days will it take for

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: amount of a radioactive tracer remaining after t days is given by A=A0e^-0.058t, where A0 is the starting amount at the beginning of the time period. how many days will it take for      Log On


   

Question 63050: amount of a radioactive tracer remaining after t days is given by A=A0e^-0.058t, where A0 is the starting amount at the beginning of the time period. how many days will it take for one half of the original amount of decay?
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
amount of a radioactive tracer remaining after t days is given by A=Aoe^-0.058t, where Ao is the starting amount at the beginning of the time period. how many days will it take for one half of the original amount of decay?
A=(1/2)Ao
%281%2F2%29Ao=Aoe%5E%28-0.058t%29
%281%2F2%29Ao%2FAo=Aoe%5E%28-0.058t%29%2FAo
1%2F2=e%5E%28-0.058t%29
ln%281%2F2%29=ln%28e%5E%28-0.058t%29%29
ln%281%2F2%29=-0.058tln%28e%29 ln(e)=1
ln%281%2F2%29=-0.058t%281%29
ln%281%2F2%29%2F-0.058=-0.058t%2F-0.058
-ln%281%2F2%29%2F0.058=t
t=11.95081346
About 12 days.
Happy Calculating!!!